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Proof step 95 from proof bits2bits-sgn (previous step)

b2i(i2b(bits2int(lastn(8, bits)))) < 0, bits2int(lastn(8, bits)) < 0, 8 < # bits, ~128 ≤ bits2int(lastn(8, bits)), ∀ bits0. # bits0 < # bits → true → bits0 = [] ∨ sgn(bytes2bits(bits2bytes(bits0))) = sgn(bits0) ⊦ # lastn(8, bits) = 8, sgn(byte2bits(i2b(bits2int(lastn(8, bits))))) = sgn(bits), bits = [], false ∈ bytes2bits(bits2bytes(firstn(# bits - 8, bits))), false ∈ firstn(# bits - 8, bits)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 96:
⊦ n ≤ # bits → # lastn(n, bits) = n

Rule argument

seq: ⊦ n ≤ # bits → # lastn(n, bits) = n subst: [bits, n] → [bits, 8] rotate: F spec: list-del inst: bitlista name: lastN-length

Additional information

Used simplifier rules: ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n → ¬ n < m; Used terms: bits, 8